Bridging the gap between clinical applications and mathematical models is one of the new challenges of medical image analysis. In this paper, we propose an efficient and accurate algorithm to solve anisotropic Eikonal equations, in order to link biological models using reaction-diffusion equations to clinical observations, such as medical images. The example application we use to demonstrate ou...

Nucleus-nucleus scattering is studied in the local Reggeon Field Theory in the quasi-classical approximation with non-eikonal boundary conditions corresponding to the Glauber picture at low energies. Comparison with the commonly used eikonal boundary conditions shows that the new conditions make both the action and nucleus-nucleus total cross-sections lower by 3÷ 5 %. They also substantially ch...

A new class of non-linear O(3) models is introduced. It is shown that these systems lead to integrable submodels if an additional integrability condition (so called the generalized eikonal equation) is imposed. In the case of particular members of the family of the models the exact solutions describing toroidal solitons with a non-trivial value of the Hopf index are obtained. Moreover, the gene...

The gravity effects in high-energy scattering, described by a fourdimensional eikonal amplitude related to gravireggeons induced by compact extra dimensions are studied. It is demonstrated that the real part of the eikonal (with a massless mode subtracted) dominates its imaginary part at both small and large impact parameters, in contrast to the usual case of hadronic high-energy behavior. The ...

In this paper we propose an adaptation of the static eikonal equation over weighted graphs of arbitrary structure using a framework of discrete operators. Based on this formulation, we provide explicit solutions for the L1,L2 and L∞ norms. Efficient algorithms to compute the explicit solution of the eikonal equation on graphs are also described. We then present several applications of our metho...

Recently, it was shown by Jevicki, Kazama and Yoneya (JKY) that the SuperYang-Mills theories (SYM) in D ≤ 4 can reproduce the conformal symmetry of the near-horizon geometry of the D-brane solutions. However, the eikonal approximation they used is not sufficient for analyzing the conformal symmetry in SYM. We carry out the 1-loop calculation beyond the eikonal approximation for D = 1 SYM (i.e.,...

There have been many approaches to this end. An electrical wave travelling through heterogeneous heart tissue is usually simulated using a sophisticated system of coupled ODEs and PDEs. These equations are solved on a realistic geometric mesh with numerical schemes (an example using finite element techniques is shown in §1.1). In cases where a fast approximation to the wave dynamics is needed, ...

The transformation of the eikonal equation from depth coordinates (z, x) into verticaltraveltime coordinates (τ ,ξ ) enables the computation of reflections traveltimes independent of depth-mapping. This separation allows the focusing and mapping steps to be performed sequentially even in the presence of complex velocity functions, that otherwise would “require” depth migration. The traveltimes ...

The point-source traveltime field has an upwind singularity at the source point. Consequently, all formally high-order, finite-difference eikonal solvers exhibit firstorder convergence and relatively large errors. Adaptive upwind finite-difference methods based on high-order Weighted Essentially NonOscillatory (WENO) RungeKutta difference schemes for the paraxial eikonal equation overcome this ...

In the high frequency regime, the geometrical-optics approximation for the Helmholtz equation with a point source results in an eikonal equation for traveltime and a transport equation for amplitude. Because the point-source traveltime field has an upwind singularity at the source point, all formally high-order finite-difference eikonal solvers exhibit first-order convergence and relatively lar...